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elim-eqs

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
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Nikolaj Bjorner 2020-01-05 16:45:21 -08:00
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/*++
Copyright (c) 2020 Microsoft Corporation
Module Name:
sat_aig_simplifier.cpp
Abstract:
extract AIG definitions from clauses
Perform cut-set enumeration to identify equivalences.
Author:
Nikolaj Bjorner 2020-01-02
--*/
#pragma once;
#include "util/union_find.h"
#include "sat/sat_aig_simplifier.h"
#include "sat/sat_xor_finder.h"
#include "sat/sat_elim_eqs.h"
namespace sat {
struct aig_simplifier::report {
aig_simplifier& s;
aig_cuts& c;
stopwatch m_watch;
report(aig_simplifier& s, aig_cuts& c): s(s), c(c) { m_watch.start(); }
~report() {
IF_VERBOSE(2,
verbose_stream() << "(sat.aig-simplifier"
<< " :num-eqs " << s.m_stats.m_num_eqs
<< " :num-cuts " << s.m_stats.m_num_cuts
<< " :mb " << mem_stat()
<< m_watch
<< ")\n");
}
};
void aig_simplifier::operator()() {
aig_cuts aigc;
report _report(*this, aigc);
TRACE("aig_simplifier", s.display(tout););
clauses2aig(aigc);
aig2clauses(aigc);
}
/**
\brief extract AIG definitions from clauses
Ensure that they are sorted and variables have unique definitions.
*/
void aig_simplifier::clauses2aig(aig_cuts& aigc) {
struct aig_def {
literal head;
bool_op op;
unsigned sz;
unsigned offset;
aig_def(literal h, bool_op op, unsigned sz, unsigned o): head(h), op(op), sz(sz), offset(o) {}
};
svector<aig_def> aig_defs;
literal_vector literals;
std::function<void (literal head, literal_vector const& ands)> on_and =
[&,this](literal head, literal_vector const& ands) {
aig_defs.push_back(aig_def(head, and_op, ands.size(), literals.size()));
literals.append(ands);
m_stats.m_num_ands++;
};
std::function<void (literal head, literal c, literal t, literal e)> on_ite =
[&,this](literal head, literal c, literal t, literal e) {
aig_defs.push_back(aig_def(head, ite_op, 3, literals.size()));
literal args[3] = { c, t, e };
literals.append(3, args);
m_stats.m_num_ites++;
};
aig_finder af(s);
af.set(on_and);
af.set(on_ite);
clause_vector clauses(s.clauses());
af(clauses);
literal_vector _xors;
std::function<void (literal_vector const&)> on_xor =
[&,this](literal_vector const& xors) {
SASSERT(xors.size() > 1);
unsigned max_level = s.def_level(xors.back().var());
unsigned index = xors.size() - 1;
for (unsigned i = index; i-- > 0; ) {
literal l = xors[i];
if (s.def_level(l.var()) > max_level) {
max_level = s.def_level(l.var());
index = i;
}
}
// head + t1 + t2 + .. = 1
// <=>
// ~head = t1 + t2 + ..
literal head = ~xors[index];
unsigned sz = xors.size() - 1;
aig_defs.push_back(aig_def(head, xor_op, sz, literals.size()));
for (unsigned i = xors.size(); i-- > 0; ) {
if (i != index)
literals.push_back(xors[i]);
}
m_stats.m_num_xors++;
};
xor_finder xf(s);
xf.set(on_xor);
xf(clauses);
svector<bool> outs(s.num_vars(), false);
svector<bool> ins(s.num_vars(), false);
for (auto a : aig_defs) {
outs[a.head.var()] = true;
}
for (auto a : aig_defs) {
for (unsigned i = 0; i < a.sz; ++i) {
unsigned v = literals[a.offset+i].var();
if (!outs[v]) ins[v] = true;
}
}
std::function<void(aig_def)> force_var = [&, this] (aig_def a) {
for (unsigned i = 0; i < a.sz; ++i) {
unsigned v = literals[a.offset + i].var();
if (!ins[v]) {
aigc.add_var(v);
ins[v] = true;
}
}
};
std::function<void(unsigned)> add_var = [&, this] (unsigned v) {
if (!outs[v] && ins[v]) {
aigc.add_var(v);
outs[v] = true;
}
};
for (auto a : aig_defs) {
for (unsigned i = 0; i < a.sz; ++i) {
add_var(literals[a.offset+i].var());
}
}
while (true) {
unsigned j = 0;
for (auto a : aig_defs) {
bool visited = true;
for (unsigned i = 0; visited && i < a.sz; ++i) {
visited &= ins[literals[a.offset + i].var()];
}
unsigned h = a.head.var();
if (!ins[h] && visited) {
ins[h] = true;
aigc.add_node(a.head, a.op, a.sz, literals.c_ptr() + a.offset);
}
else if (!ins[h]) {
aig_defs[j++] = a;
}
else {
TRACE("aig_simplifier", tout << "skip " << a.head << " == .. \n";);
force_var(a);
}
}
if (j == 0) {
break;
}
if (j == aig_defs.size()) {
IF_VERBOSE(2, verbose_stream() << "break cycle " << j << "\n");
force_var(aig_defs.back());
}
aig_defs.shrink(j);
}
}
void aig_simplifier::aig2clauses(aig_cuts& aigc) {
vector<cut_set> cuts = aigc.get_cuts(m_config.m_max_cut_size, m_config.m_max_cutset_size);
map<cut const*, unsigned, cut::hash_proc, cut::eq_proc> cut2id;
literal_vector roots(s.num_vars(), null_literal);
union_find_default_ctx ctx;
union_find<> uf(ctx);
for (unsigned i = 2*s.num_vars(); i--> 0; ) uf.mk_var();
auto add_eq = [&](literal l1, literal l2) {
uf.merge(l1.index(), l2.index());
uf.merge((~l1).index(), (~l2).index());
};
unsigned old_num_eqs = m_stats.m_num_eqs;
for (unsigned i = cuts.size(); i-- > 0; ) {
m_stats.m_num_cuts += cuts[i].size();
for (auto& cut : cuts[i]) {
unsigned j = 0;
if (cut2id.find(&cut, j)) {
VERIFY(i != j);
literal v(i, false);
literal w(j, false);
add_eq(v, w);
TRACE("aig_simplifier", tout << v << " == " << ~w << "\n";);
++m_stats.m_num_eqs;
break;
}
cut.negate();
if (cut2id.find(&cut, j)) {
literal v(i, false);
literal w(j, true);
add_eq(v, w);
TRACE("aig_simplifier", tout << v << " == " << w << "\n";);
++m_stats.m_num_eqs;
break;
}
cut.negate();
cut2id.insert(&cut, i);
}
}
if (old_num_eqs == m_stats.m_num_eqs) {
return;
}
bool_var_vector to_elim;
for (unsigned i = s.num_vars(); i-- > 0; ) {
literal l1(i, false);
unsigned idx = uf.find(l1.index());
if (idx != l1.index()) {
roots[i] = to_literal(idx);
to_elim.push_back(i);
}
else {
roots[i] = l1;
}
}
elim_eqs elim(s);
elim(roots, to_elim);
}
void aig_simplifier::collect_statistics(statistics& st) const {
st.update("sat-aig.eqs", m_stats.m_num_eqs);
st.update("sat-aig.cuts", m_stats.m_num_cuts);
st.update("sat-aig.ands", m_stats.m_num_ands);
st.update("sat-aig.ites", m_stats.m_num_ites);
st.update("sat-aig.xors", m_stats.m_num_xors);
}
vector<cut_set> aig_cuts::get_cuts(unsigned max_cut_size, unsigned max_cutset_size) {
unsigned_vector sorted = top_sort();
vector<cut_set> cuts;
cuts.resize(m_aig.size());
max_cut_size = std::min(cut::max_cut_size, max_cut_size);
cut_set cut_set2;
cut_set2.init(m_region, max_cutset_size + 1);
for (unsigned id : sorted) {
node const& n = m_aig[id];
if (!n.is_valid()) {
continue;
}
auto& cut_set = cuts[id];
cut_set.init(m_region, max_cutset_size + 1);
if (n.is_var()) {
SASSERT(!n.sign());
}
else if (n.is_ite()) {
literal l1 = child(n, 0);
literal l2 = child(n, 1);
literal l3 = child(n, 2);
for (auto const& a : cuts[l1.var()]) {
for (auto const& b : cuts[l2.var()]) {
cut ab;
if (!ab.merge(a, b, max_cut_size)) {
continue;
}
for (auto const& c : cuts[l3.var()]) {
cut abc;
if (!abc.merge(ab, c, max_cut_size)) {
continue;
}
if (cut_set.size() >= max_cutset_size) break;
uint64_t t1 = a.shift_table(abc);
uint64_t t2 = b.shift_table(abc);
uint64_t t3 = c.shift_table(abc);
if (l1.sign()) t1 = ~t1;
if (l2.sign()) t2 = ~t2;
if (l3.sign()) t3 = ~t3;
abc.set_table((t1 & t2) | (~t1 & t3));
if (n.sign()) abc.negate();
// extract tree size: abc.m_tree_size = a.m_tree_size + b.m_tree_size + c.m_tree_size + 1;
cut_set.insert(abc);
}
}
}
}
else if (n.num_children() == 2) {
SASSERT(n.is_and() || n.is_xor());
literal l1 = child(n, 0);
literal l2 = child(n, 1);
for (auto const& a : cuts[l1.var()]) {
for (auto const& b : cuts[l2.var()]) {
if (cut_set.size() >= max_cutset_size) break;
cut c;
if (c.merge(a, b, max_cut_size)) {
uint64_t t1 = a.shift_table(c);
uint64_t t2 = b.shift_table(c);
if (l1.sign()) t1 = ~t1;
if (l2.sign()) t2 = ~t2;
uint64_t t3 = n.is_and() ? t1 & t2 : t1 ^ t2;
c.set_table(t3);
if (n.sign()) c.negate();
cut_set.insert(c);
}
}
if (cut_set.size() >= max_cutset_size) break;
}
}
else if (n.num_children() < max_cut_size) {
SASSERT(n.is_and() || n.is_xor());
literal lit = child(n, 0);
for (auto const& a : cuts[lit.var()]) {
cut_set.push_back(a);
if (lit.sign()) {
cut_set.back().negate();
}
}
for (unsigned i = 1; i < n.num_children(); ++i) {
cut_set2.reset();
literal lit = child(n, i);
for (auto const& a : cut_set) {
for (auto const& b : cuts[lit.var()]) {
cut c;
if (cut_set2.size() >= max_cutset_size)
break;
if (c.merge(a, b, max_cut_size)) {
uint64_t t1 = a.shift_table(c);
uint64_t t2 = b.shift_table(c);
if (lit.sign()) t2 = ~t2;
uint64_t t3 = n.is_and() ? t1 & t2 : t1 ^ t2;
c.set_table(t3);
if (i + 1 == n.num_children() && n.sign()) c.negate();
cut_set2.insert(c);
}
}
if (cut_set2.size() >= max_cutset_size)
break;
}
cut_set.swap(cut_set2);
}
}
cut_set.push_back(cut(id));
}
return cuts;
}
void aig_cuts::add_var(unsigned v) {
m_aig.reserve(v + 1);
m_aig[v] = node(v);
SASSERT(m_aig[v].is_valid());
}
void aig_cuts::add_node(literal head, bool_op op, unsigned sz, literal const* args) {
TRACE("aig_simplifier", tout << head << " == " << op << " " << literal_vector(sz, args) << "\n";);
unsigned v = head.var();
m_aig.reserve(v + 1);
m_aig[v] = node(head.sign(), op, sz, m_literals.size());
m_literals.append(sz, args);
DEBUG_CODE(
for (unsigned i = 0; i < sz; ++i) {
SASSERT(m_aig[args[i].var()].is_valid());
});
SASSERT(m_aig[v].is_valid());
}
unsigned_vector aig_cuts::top_sort() {
unsigned_vector result;
svector<bool> visit;
visit.reserve(m_aig.size(), false);
unsigned_vector todo;
unsigned id = 0;
for (node const& n : m_aig) {
if (n.is_valid()) todo.push_back(id);
++id;
}
while (!todo.empty()) {
unsigned id = todo.back();
if (visit[id]) {
todo.pop_back();
continue;
}
bool all_visit = true;
node const& n = m_aig[id];
SASSERT(n.is_valid());
if (!n.is_var()) {
for (unsigned i = 0; i < n.num_children(); ++i) {
bool_var v = child(n, i).var();
if (!visit[v]) {
todo.push_back(v);
all_visit = false;
}
}
}
if (all_visit) {
visit[id] = true;
result.push_back(id);
todo.pop_back();
}
}
return result;
}
}

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/*++
Copyright (c) 2020 Microsoft Corporation
Module Name:
sat_aig_simplifier.h
Abstract:
extract AIG definitions from clauses
Perform cut-set enumeration to identify equivalences.
Author:
Nikolaj Bjorner 2020-01-02
--*/
#pragma once;
#include "sat/sat_aig_finder.h"
#include "sat/sat_cutset.h"
namespace sat {
enum bool_op {
var_op,
and_op,
ite_op,
xor_op,
no_op
};
class aig_cuts {
// encodes one of var, n1 & n2 & .. & nk, !(n1 & n2 & .. & nk)
class node {
bool m_sign;
bool_op m_op;
unsigned m_num_children;
unsigned m_offset;
public:
node(): m_sign(false), m_op(no_op), m_num_children(UINT_MAX), m_offset(UINT_MAX) {}
explicit node(unsigned v): m_sign(false), m_op(var_op), m_num_children(UINT_MAX), m_offset(v) {}
explicit node(bool negate, bool_op op, unsigned num_children, unsigned offset):
m_sign(negate), m_op(op), m_num_children(num_children), m_offset(offset) {}
bool is_valid() const { return m_offset != UINT_MAX; }
bool_op op() const { return m_op; }
bool is_var() const { return m_op == var_op; }
bool is_and() const { return m_op == and_op; }
bool is_xor() const { return m_op == xor_op; }
bool is_ite() const { return m_op == ite_op; }
unsigned var() const { SASSERT(is_var()); return m_offset; }
bool sign() const { return m_sign; }
unsigned num_children() const { SASSERT(!is_var()); return m_num_children; }
unsigned offset() const { return m_offset; }
};
svector<node> m_aig; // vector of aig nodes.
literal_vector m_literals;
region m_region;
unsigned_vector top_sort();
public:
void add_var(unsigned v);
void add_node(literal head, bool_op op, unsigned sz, literal const* args);
literal child(node const& n, unsigned idx) const { SASSERT(!n.is_var()); SASSERT(idx < n.num_children()); return m_literals[n.offset() + idx]; }
vector<cut_set> get_cuts(unsigned max_cut_size, unsigned max_cutset_size);
};
class aig_simplifier {
public:
struct stats {
unsigned m_num_eqs, m_num_cuts, m_num_xors, m_num_ands, m_num_ites;
stats() { reset(); }
void reset() { memset(this, 0, sizeof(*this)); }
};
struct config {
unsigned m_max_cut_size;
unsigned m_max_cutset_size;
config(): m_max_cut_size(4), m_max_cutset_size(10) {}
};
private:
solver& s;
stats m_stats;
config m_config;
struct report;
void clauses2aig(aig_cuts& aigc);
void aig2clauses(aig_cuts& aigc);
public:
aig_simplifier(solver& s) : s(s) {}
~aig_simplifier() {}
void operator()();
void collect_statistics(statistics& st) const;
};
}